Synaptic Static

The Mathematics of a Striking Moonrise

mathematics

astronomy

celestial-mechanics

A first-principles derivation of solar and lunar position, rise/set times, and the geometry that produces a perfect moonrise — with interactive visualizers.

The Arcane Boiler: Powering Industrialization with ‘Heat Metal’

Estimations

D&D

Engineering

In Dungeons & Dragons 5e, the spell Heat Metal is a low-level staple for cooking enemies in their own armor. The spell description states: “you cause a metal object to glow…

Connor Lockhart

The Slushee Phase-Change Optimization

Estimations

Thermodynamics

Have you ever reached the end of an Icee or Slurpee only to find a desolate, dry block of white ice? This is the “Slushee Dead Zone”—a state where the liquid-to-solid ratio…

Connor Lockhart

The Parking Ticket Expected Value: A Poisson Process Estimation

Musings

Estimations

I was parking my car today and while I was enroute to proctor an exam for my probability class, I had a curious idea. I was wondering what an expected value argument would…

Connor Lockhart

Discrete and Stochastic Structures in Hyperbolic Geometry

Academic Work

Mathematics

Hyperbolic Geometry

My research focuses on the intersection of model theory, topology, and stochastic geometry, specifically through the lens of structures embedded in hyperbolic space. Two…

Connor Lockhart

The Laundry Quarter Recurrence: A Birthday Problem Estimation

Musings

Estimations

Have you ever wondered if the quarter you just dropped into the laundry machine is one you’ve held before? A friend recently asked me this very question. A solution can be…

Connor Lockhart